The fullback has joined Madrid from Real Sociedad.
After a summer in which Cristiano Ronaldo and Zinedine Zidane departed, Perez was keen to accentuate the positives.
"Odriozola has chosen to come to the most demanding club," he said to reporters.
"He will never forget that Real Madrid never gives up and here we want you to be happy.
"This is the dream and the great challenge of your career, thank you for choosing us.
"We have a great squad that is going to be reinforced with fantastic players, and Alvaro was clear about where he wanted to play."